Modeling Nonstationary Time Series and Inferring Instantaneous Dependency, Feedback and Causality: An Application to Human Epileptic Seizure Event Data

Abstract

Abstract The parametric modeling of nonstationary covariance time series and the determination of the instantaneously changing structure of the interdependencies between those time series, inferred from the fitted model are treated. The nonstationary time series are modeled by a multivariate time varying autoregressive (AR) model. The time evolution of the AR parameters are expressed as linear combinations of discrete Legendre orthogonal polynomial functions of time. The model is fitted by a Householder t|ransformat ion least squares-Akaike AIC order determination, regression subset selection method. The computation of the instantaneous dependence, feedback and causality structure of the time series, from the fitted model, is discussed. An example of the modeling and determination of instantaneous causality in a human implanted electrode seizure event EEG is shown.